$x-2 y-6=0$ is a normal to the circle $x^{2}+y^{2}+2 g x+2 f y-8=0$. If the line $y=2$ touches this circle, then the radius of the circle can be

The line $x+y+1=0$ intersects the circle $x^{2}+y^{2}-4 x+2 y-4=0$ at the points $A$ and $B$. If $M(a, b)$ is the mid-point of $A B$, then $a-b=$

A circle $S$ passes through the points of intersection of the circles $x^{2}+y^{2}-2 x-3=0$ and $x^{2}+y^{2}-2 y=0$. If $x+y+1=0$ is a tangent to the circle $S$, then equation of $S$ is

If the common chord of the circles $x^{2}+y^{2}-2 x+2 y+1=0$ and $x^{2}+y^{2}-2 x-2 y-2=0$ is the diameter of a circle $S$, then the center of the circles is